310 miles is too low
Geo synchronous is too high - and a silly idea anyway
What you want is something mid range, - GPS have about a 6 hour orbital period, I imagine an 8 hour period would work well so long as you use multiple units to hand off duties as the geometry progressed.
The whole system would need to be dynamic, not a static mirror sitting over the target but multiple satellites radically changing orientation continually through out their journey. Think intricate clockwork.
This would have the advantage of being useful for more than a single city
but it is still a really bad idea from an environmental perspective - it will burn out every organism that regulates its life from a lunar cycle - and the lightspill pollution will be far more widespread than any ground level illuminated site.